P1.T2 BT 300.2 question

[Thomas Obitz]

Hi,

sorry for being a bit pedantic, but I am not quite sure whether the answer to P1.T2 BT 300.2 is right. If the PDF describes the distribution of potential paybacks, the 5% quantile is 1.842 and the nominal value is $5, wouldn't the 5% VaR be - (1.842 - 5) = 3.158?

Regards
Thomas

 

[David Harper CFA FRM]

Hi @Thomas Obitz sorry for the delay (working off some of the backlog ....). I don't think it's pedantic, I think you are totally correct. The question gets lazy, it is:

If we apply the inverse cumulative distribution function and find the price of the bond (i.e., the value of x) such that 5.0% of the distribution is less than or equal to (x), what is this price; in other words, since this is a 5% quantile function, what is the 95% value at risk (VaR)?

The question looks fine up to "what is the price?" which merely queries the quantile (and is consistent with Miller, the source here). But, geez, I'm quite wrong to equate that with "what is the 95% value at risk (VaR)?" exactly as you suggest. For one thing, if the quantile of the bond's future value were VaR, then VaR would mistakenly decrease with higher confidence. I agree with your expression above, that is best.

I've tagged the Q&A for revision (this set does have an upcoming revision), thanks for the helpful correction!